How do modal syllogisms include ideas of necessity and possibility?

In the context of ancient logic, modal syllogisms are syllogisms in which the component categorical propositions include expressions of necessity or possibility. While standard assertoric syllogisms state that a predicate simply belongs or does not belong to a subject, modal syllogisms specify that a predicate belongs (or does not) necessarily or possibly to some or every subject.12

Aristotle initiated the study of these syllogisms by testing how modal categoricals could be integrated into the valid moods of his assertoric syllogistic. He defined the "possible" in two ways:1
* As the opposite of the impossible (what is not impossible).1
* As the contingent (what is neither necessary nor impossible).1

In his modal syllogistic, Aristotle generally used the second sense for premises, though he occasionally employed the first in conclusions. His successor, Theophrastus, later simplified this theory by adopting only the first definition of possibility and establishing a rule that the conclusion of a modal syllogism cannot be stronger than its weakest premise. These systems represent an early attempt to formalize logical arguments involving modal concepts, distinct from the noncategorical, propositional logic later developed by the Stoics.1342